Rekenen met wortels (reeks 5)

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Maak de noemer wortelvrij

1. \(\frac{30}{\sqrt{3}}\)
2. \(\frac{55}{\sqrt{11}}\)
3. \(\frac{22}{\sqrt{7}}\)
4. \(\frac{16}{\sqrt{7}}\)
5. \(\frac{31}{\sqrt{17}}\)
6. \(\frac{25}{\sqrt{2}}\)
7. \(\frac{32}{\sqrt{14}}\)
8. \(\frac{46}{\sqrt{15}}\)
9. \(\frac{35}{\sqrt{3}}\)
10. \(\frac{44}{\sqrt{2}}\)
11. \(\frac{7}{\sqrt{7}}\)
12. \(\frac{51}{\sqrt{3}}\)

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Maak de noemer wortelvrij

Verbetersleutel

1. \(\frac{30}{\sqrt{3}}=\frac{30\cdot \color{red}{\sqrt{3}} }{\sqrt{3}\cdot \color{red}{\sqrt{3}} }=\frac{30\cdot\sqrt{3}}{3}=10\cdot\sqrt{3}\)
2. \(\frac{55}{\sqrt{11}}=\frac{55\cdot \color{red}{\sqrt{11}} }{\sqrt{11}\cdot \color{red}{\sqrt{11}} }=\frac{55\cdot\sqrt{11}}{11}=5\cdot\sqrt{11}\)
3. \(\frac{22}{\sqrt{7}}=\frac{22\cdot \color{red}{\sqrt{7}} }{\sqrt{7}\cdot \color{red}{\sqrt{7}} }=\frac{22\cdot\sqrt{7}}{7}\)
4. \(\frac{16}{\sqrt{7}}=\frac{16\cdot \color{red}{\sqrt{7}} }{\sqrt{7}\cdot \color{red}{\sqrt{7}} }=\frac{16\cdot\sqrt{7}}{7}\)
5. \(\frac{31}{\sqrt{17}}=\frac{31\cdot \color{red}{\sqrt{17}} }{\sqrt{17}\cdot \color{red}{\sqrt{17}} }=\frac{31\cdot\sqrt{17}}{17}\)
6. \(\frac{25}{\sqrt{2}}=\frac{25\cdot \color{red}{\sqrt{2}} }{\sqrt{2}\cdot \color{red}{\sqrt{2}} }=\frac{25\cdot\sqrt{2}}{2}\)
7. \(\frac{32}{\sqrt{14}}=\frac{32\cdot \color{red}{\sqrt{14}} }{\sqrt{14}\cdot \color{red}{\sqrt{14}} }=\frac{32\cdot\sqrt{14}}{14}=\frac{16\cdot\sqrt{14}}{7}\)
8. \(\frac{46}{\sqrt{15}}=\frac{46\cdot \color{red}{\sqrt{15}} }{\sqrt{15}\cdot \color{red}{\sqrt{15}} }=\frac{46\cdot\sqrt{15}}{15}\)
9. \(\frac{35}{\sqrt{3}}=\frac{35\cdot \color{red}{\sqrt{3}} }{\sqrt{3}\cdot \color{red}{\sqrt{3}} }=\frac{35\cdot\sqrt{3}}{3}\)
10. \(\frac{44}{\sqrt{2}}=\frac{44\cdot \color{red}{\sqrt{2}} }{\sqrt{2}\cdot \color{red}{\sqrt{2}} }=\frac{44\cdot\sqrt{2}}{2}=22\cdot\sqrt{2}\)
11. \(\frac{7}{\sqrt{7}}=\frac{7\cdot \color{red}{\sqrt{7}} }{\sqrt{7}\cdot \color{red}{\sqrt{7}} }=\frac{7\cdot\sqrt{7}}{7}=\frac{\sqrt{7}}{1}\)
12. \(\frac{51}{\sqrt{3}}=\frac{51\cdot \color{red}{\sqrt{3}} }{\sqrt{3}\cdot \color{red}{\sqrt{3}} }=\frac{51\cdot\sqrt{3}}{3}=17\cdot\sqrt{3}\)